Jimmy Savile with students from Manchester University in 1964. Photograph: Popperfoto/Getty Images

"Some time after the cock crows on the morning of 7 November, Mitt Romney will be declared America's 45th president," Karl Rove predicted a few days before he wasn't. Implacable faith in a Romney win, even a landslide, was commonplace among US conservatives this year, among them Newt Gingrich, Glenn Beck and Donald Trump. ("Mitt Romney wins… decisively," promised the commentator Andrew McCarthy, the author of a book about terrorism entitled – no, really! – Willful Blindness.) But Rove's wake-up call, in the end, came long before the cock crowed, late on 6 November, and his meltdown live on Fox News said it all: the facts just didn't compute. This wasn't only a problem among pundits: Romney's own strategists, it later emerged, had been so immersed in their echo-chambers, on Twitter and in the rightwing blogosphere, that they'd felt "shellshocked", as one of them put it, when the polls were proved correct. Romney boasted that he'd only written a victory speech. Reality wasn't invited to his election night party in Boston, but it gatecrashed anyway.

There's no shame in making a mistaken prediction, nor even in spinning things positively for your team. But US politics in 2012 was characterised by something more radical: a steadfast, fingers-in-the-ears refusal to hear basic and obvious facts on which everyone, under any normal circumstances, would have agreed. Truth-tellers were vilified: the New York Times's in-house statistics geek, Nate Silver, persistently predicted a Barack Obama victory – and so it was clear, to those inside the rightwing bubble, that he must be biased. (And also insufficiently manly: "Nate Silver is a man of very small stature, a thin and effeminate man with a soft-sounding voice," explained Dean Chambers, the man behind UnSkewed Polls, a site that achieved viral popularity by adjusting the numbers, shamelessly, in favour of Republicans.) Reality was unacceptable, and so it had to be denied.

Laughing at America's conservatives can be a nourishing and noble pursuit. But isn't this denial of reality also, essentially, how Jimmy Savile evaded scrutiny for decades, and perhaps why Newsnight spiked its investigation into his alleged crimes?

Savile wasn't a man who concealed his creepiness behind a respectable facade. Creepiness was his brand; looking back now, it's as if he was daring the world to point out that he seemed so much like a sex offender. Neville Thurlbeck, the former News of the World reporter, claimed that Savile had a "joke" he'd wheel out whenever Thurlbeck phoned: "Oh no, not the News Of The World – she told me she was 16 years old!" The horror was hiding in plain sight. But acknowledging it would have meant acknowledging exactly who it was that we'd elevated to the status of national treasure – or perhaps even acknowledging, as Andrew O'Hagan put it in the London Review of Books, "that the culture itself is largely paedophile in its commercial and entertainment excitements".

This refusal to see what we're looking at is surely at the heart of climate-change denial, too, and it's here that the phenomenon seems easiest to psychoanalyse: who wouldn't prefer to convince themselves, if only they were able to, that global catastrophe isn't on the cards? (Not that those of us who accept the science are necessarily off the hook. Do you feel actively scared, on a daily basis, by global warming? I don't, and maybe that's its own form of denial.)

The annals of psychological research are full of examples of how accomplished we are at not seeing what's there, for many reasons. People given the opportunity to cheat in small ways on tests, for example, don't consciously acknowledge they're dishonest; they'd rather preserve their sense of not being cheats. Or perhaps you've seen that famous basketball video demonstrating the phenomenon of "change blindness": when people are asked to count the number of times the ball is passed between players, they fail to see a person in a gorilla suit walk right across the frame.

Denial, in a broader sense, has its benefits: without a dose of it, we'd be unable to overlook our own and others' lapses and faults, and relationships would become impossible. But its pitfalls are enormous, as Romney's aides and media supporters learned. Or did they learn? Within a day of defeat, Dick Morris, the former aide to Bill Clinton turned strident Republican, was finding ways to acknowledge the disaster while clinging to unreality. What changed everything, he and others concluded, was Superstorm Sandy: before that, Romney had been on course to win. Except – guess what? – he hadn't been. As Silver showed, Obama not only had the lead, but also the momentum, prior to Sandy's arrival. Denial dies hard.

"Ohio really did go to President Obama last night. And he really did win. And he really was born in Hawaii," Rachel Maddow of MSNBC informed Republicans the morning after the election. "And he really is legitimately president of the United States… There are real problems in the world. There are real knowable facts in the world." The dream scenario for 2013 is that we might stop dreaming.